Finding a point part way between two points  Analytic geometry  Geometry  Khan Academy  Summary and Q&A
TL;DR
Find point B on segment AC such that the ratio of AB to BC is 3:1.
Questions & Answers
Q: How can the problem of finding point B be approached?
The problem can be approached by breaking it down into horizontal and vertical changes between points A and C. We can calculate the horizontal and vertical distances separately to find B.
Q: What are the horizontal and vertical distances between points A and C?
The horizontal distance between A and C is 16 units, while the vertical distance is 4 units.
Q: How can we determine the coordinates of point B?
To find the coordinates of point B, we need to move 1/4 of the way from C to A both vertically and horizontally. This will result in the coordinates (3, 2) for point B.
Q: How can we visually determine the position of point B on the line segment?
We can visually determine the position of point B by marking the 1/4 distance on either the horizontal or vertical axis and finding the intersection point on the line segment.
Summary & Key Takeaways

The task is to find point B on segment AC, with a specific ratio of AB to BC.

The distance between B and A is 3 times the distance between B and C.

The problem can be solved by breaking it down into vertical and horizontal changes between point A and point C.